Spectral Form Factor as an OTOC Averaged over the Heisenberg Group

Abstract

We prove that in bosonic quantum mechanics the two-point spectral form factor can be obtained as an average of the two-point out-of-time ordered correlation function, with the average taken over the Heisenberg group. In quantum field theory, there is an analogous result with the average taken over the tensor product of many copies of the Heisenberg group, one copy for each field mode. The resulting formula is expressed as a path integral over two fields, providing a promising approach to the computation of the spectral form factor. We develop the formula that we have obtained using a coherent state description from the JC model and also in the context of the large-$N$ limit of CFT and Yang-Mills theory from the large-$N$ matrix quantum mechanics.

16 pages, minor changes, reference added

References in corpus (4)

• Anderson Transitions
• Measurement of many-body chaos using a quantum clock
• Interferometric Approach to Probing Fast Scrambling
• Quantum bound to chaos and the semiclassical limit

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• Bipartite OTOC in open quantum systems: information scrambling and irreversibility
• Detecting quantum chaos via pseudo-entropy
• Interferometric and Bipartite OTOC for Non-Markovian Open Quantum Spin-Chains and Lipkin-Meshkov-Glick Model